Now we discuss the \(M\)  deformation with the shift put at a branch point. To motivate the construction, we first review, following [1]}, the corresponding deformation of the unorbifolded \(T^2\times \mathbb {C}\)  background, \(\eta ^2 = P\) . Put the \(M\)  shift at the Weierstrass point \(w=0\)  (which is \(x=\infty \)  in the \(w=1\)  patch) by defining the transition map,
\(\widetilde{v} = v + M \frac{\eta }{w x} ,\) 
